Farmer had 100 rabbits, and every month foxes stole 20 rabbits?

Question

This equlilibrium state of affairs contiued for quite a while until on January 1 2006 the farmer fixed the holes in the fence, so that foxes could no longer enter.

How many rabbits will be there on January 1, 2008?

Answer 1

Let's assume all rabbits are capable of breeding, and they produce additional rabbits each month proportional to their population. Let's also assume the farmer has 100 rabbits at the end of each month, and on the first day of each month, the foxes have stolen 30 rabbits, and also that each month is exactly 1/12 of the year.

So, the rabbit population drops to 80 at the beginning of each month, but then climbs back to 100 by the end of the month. What growth rate is required to raise the population from 80 to 100 in one month?

P = Pinitial * 1.25^(t)
where t is the number of months that have elapsed. If you plug in t=1, it becomes clear that the population increases by 25% each month.

Now, on December 31, 2005, the rabbit population has climbed back to 100. The farmer fixes the fence early the next day, and the foxes never again steal any rabbits.

Then, 24 months of unbounded rabbit breeding occur. The population after this time is:

P = Pinitial * 1.25^(t)
P = 100 * 1.25^(24)
P = 100 * 211.758
P = 21175.8

So, there are about 21,176 rabbits on January 1, 2008.

Answer 2

Assuming that none die, 80 rabbits produce another 20 every month or, each month it takes 4 rabbits to produce 1 additional rabbit, which sounds kinky, but I'm assuming that 2 of the rabbits are not mature yet and the other two are....anyway, if there are 100 rabbits on 1/1/2006, on 2/1/2006 there will be 125 rabbits. This will go up by 25% each month, sort of like a principle and interest problem, where the original principle was 100, the interest rate is 300% compounded monthly, and the number of periods is 24 (all of 2006 and 2007)...so does that give you a clue about how to solve it? I came up with 21176 rabbits.

Answer 3

Rabbits reproduce like rabbits.
Tough question!

Answer 4

ANS: 0

The rabbits all ran away.